Sent: 07-09-2010 10:09:03
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Dealing with Risk Aversion
Equity investors, preoccupied with downside investment risks, are not helped by research which pretends that the costs of risk are symmetric.
Across the major advanced economy stock markets, investors seem more concerned about the return of their capital rather than the return on their capital. Risk averse investors are buying low yielding government bonds and eschewing equity investments even where analysts are forecasting strong stock price gains.
The tendency to put more emphasis on downside risk has been discussed among economists well before the current cycle.
Some 50 years ago, Paul Samuelson reported a lunch time conversation with one of his MIT academic colleagues. During the lunch, Samuelson is supposed to have asked E. Cary Brown if he would take the following bet. Samuelson would toss a coin. If it came up tails, Cary Brown would have to pay Samuelson $100. If, however, the coin came up heads, Samuelson would pay Cary Brown $200. According to Samuelson, Cary Brown refused to take the bet.
Samuelson then said he would toss the coin 100 times and offered his colleague the same opportunity: every time the coin came up tails, Cary Brown would have to pay Samuelson $100 but every time the coin showed heads, Samuelson would pay $200.
Cary Brown immediately said he would participate in the second bet. Apparently, Samuelson promptly returned to his office to write the paper later published as "Risk and Uncertainty: A Fallacy of Large Numbers" (Scientia, 98, 1963) in which he argued that his highly esteemed colleague was being irrational in his decision making.
According to Samuelson, Cary Brown probably erred in assuming that the variance of a repeated series of bets was lower than the variance of a single bet. Since then, economists have pored over decision making under uncertainty in more detail and, nowadays, would argue that the expected utility function varies for different levels of wealth.
If the same utility function were to prevail for all wealth levels, the risk averse investor might never participate in the market again because he would only accept larger bets if the prospective returns were huge. In reality, the utility function itself adjusts and people will take what, to Samuelson, had appeared as irrational decisions.
Unfortunately, most investment research fails to recognize these features of the decision-making process.
Measures of risk, for example, frequently rely on calculating the standard deviation in returns. The standard deviation measures the uncertainty inherent in returns by calculating deviations around the mean. However, to the extent that it is used as a risk measure, this widely used statistic implies investors attribute the same absolute value to a decline in share prices as they do to a rise of the same size.
In the current market environment, however, investors want to attribute a high cost to a negative investment variation and, like Cary Brown, may attribute little value to the upside potential.
This clear tendency is largely ignored by brokers when they set target prices for stocks.
One of the leading Australian institutional equity broking firms has a target price for Wesfarmers, for example, of $39.06, an implied gain over 12 months of 17%. If potential investors perceive a 30% chance of a 20% decline in the share price over the same period of time, they might be only willing to push up the price by 4.4%.
Target prices should take account of downside risks by building appropriate risk factors into the discount rates used in valuations. Conceptually, a discount rate should adjust the cost of capital for the chance that investment returns are negative. More usually, however, analysts calculate a beta factor which also assumes a symmetric cost of risk.
The same broker referred to above has used costs of equity for BHP Billiton, Wesfarmers and Brambles of 9.8%, 12.5% and 10.6%, respectively, in valuing those three companies. That implies returns from BHP Billiton will be the least risky among the three.
Since the earnings of BHP Billiton are closely linked to commodity price movements, there is some chance that its earnings will fall and its investment returns will be negative in the year ahead. The analyst is suggesting that a 9.8% return on equity from BHP Billiton would be an acceptable outcome but this also assumes that the cost of risk is symmetric, which we know it is not. If the chance of negative returns was given a higher weighting than positive returns in calculating the beta, the minimum acceptable return from BHP Billiton would be significantly higher (and target share prices consequently lower).
Against this background, we should not be surprised to see lengthy periods during which time investors seemingly ignore stock recommendations from analysts based on historical averages and an incorrect assumption about their decision making. Analysts' forecasts may eventually be right but not because of the quality of their financial modelling.
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